Acoustic radiation force on a rigid sphere exerted by a Gaussian pulsed wave.

The transient acoustic radiation force from finite-duration pulses uniquely enables superior selectivity with simple hardware and fine spatial tuning. Unfortunately, most studies on acoustic radiation force have been conducted in steady-state acoustic fields, and the transient force from finite-duration pulses has not yet been fully investigated. Therefore, a unified transient acoustic radiation force theory for arbitrary-sized objects is presented, deriving from scattering theory a closed-form solution for pulse-parameter-dependent transient forces. In the monochromatic limit, the formulation recovers the exact solutions of the acoustic radiation force function for Mie-type particles, revealing that the transient radiation force arises from the coupling between the pulse spectrum and the object's frequency-dependent scattering response. The pulse width governs the effective spectral bandwidth, while the center frequency determines how the spectrum probes scattering resonances. Their nontrivial interaction yields characteristic features, including parameter-dependent saturation, weak oscillations, and distinct strength hierarchies of regulatory effects. This theory breaks the Rayleigh scattering limit existing in previous formalisms regarding the transient radiation force, thereby providing a predictive tool for pulsed acoustic tweezers and opening new directions for pulsed wave-particle interactions.